Conventional coherent receivers in optical communication systems make use of channel equalizers to mitigate channel impairments. For example, equalizer stages can be implemented to provide a digital detector with the capability to correct channel impairments.
In this respect, modern optical communication systems can employ multi-phase multi-level signal alphabets and polarization division multiplexing (PDM) to carry high data rates with good spectral efficiency. In contrast to traditional direct demodulation, state-of-the-art coherent demodulation techniques map the impinging optical signal onto electrical signals potentially without any loss of information.
Signal processing in coherent optical receivers is customarily implemented in the equivalent complex baseband. The receiver front-end decomposes an arbitrary pair of orthogonal polarizations H and V into their in-phase (I) and quadrature (Q) components. The four resulting electrical signals HI, HQ, VI and VQ are sampled and passed to a digital processor that implements the detection algorithms.
Typical processing entails multiple stages for the mitigation of the transmission impairments. The group velocity dispersion (GVD) induced by chromatic dispersion (CD) in optic fibers can, for example, be compensated via a linear equalizer called bulk CD equalizer. Since CD acts independently of the polarization and is a quasi-static phenomenon, the bulk CD equalizers processes the H and V polarizations separately and it is generally sufficient to adjust the CD equalizers only at link set-up or in case of link reconfiguration.
By contrast, polarization dependent effects occurring in the optical fiber, such as for example polarization rotation, polarization mode dispersion (PMD) and polarization-dependent loss (PDL), are more dynamic in nature. These effects are conventionally compensated using a second linear equalizer, called multiple-input multiple-output (MIMO) equalizer, which processes jointly the H and V signals. Because of the dynamic nature of the polarization dependent effects, the MIMO equalizer can be continuously adapted to react to dynamically changing channel conditions.
Following the equalization stages, additional detection stages can include carrier frequency and phase recovery, which compensates the mismatch between transmit and receive lasers.
FIG. 1 shows a representation of digital signal processing device 100 included in a conventional coherent receiver.
The four electrical baseband tributaries (HI, HQ, VI, VQ) 110, 120, 130, 140 correspond to H and V polarizations of an optical signal, transmitted via an optical fiber, which have been received and converted to electrical baseband tributaries at the coherent receiver. In FIG. 1, the four electrical baseband tributaries (HI, HQ, VI, VQ) 110, 120, 130, 140 are sampled at Nyquist rate or faster by means of four analog-to-digital converters (ADCs) 150, 160, 170, 180. It follows that a timing misalignment (skew) among the electrical baseband tributaries (HI, HQ, VI, VQ) 110, 120, 130, 140 can arise as a consequence of imbalances in the analog paths, such as for example in the analog-to-digital converters (ADCs) 150, 160, 170, 180. The sampled signals are forwarded to configurable delays 190, 200, 210, 220, described in more detail below, and the I and Q components of both polarization planes are logically gathered in two complex signals corresponding to H and V in the equivalent complex baseband. In FIG. 1, the step of gathering the I and Q components of each polarization plane is symbolized by having multiplier blocks 230, 240 perform multiplication of the Q components by the imaginary unit j, and by a subsequent addition of the respective real and imaginary parts.
Then, each polarization plane of the complex baseband signal is passed through a complex-valued single-input single-output (SISO) bulk CD equalizer 250, 260. Here, the bulk CD equalizer 250, 260 typically corresponds to a long linear finite impulse response (FIR) filter, for example with up to 4000 complex coefficients. Due to complexity reasons, the bulk CD equalizer 250, 260 FIR filter can be implemented in the frequency domain.
Both polarization signals provided by the bulk CD equalizers 250, 260 are then jointly processed by a MIMO equalizer 270. In this example, the MIMO equalizer 270 includes a 2×2 FIR decimating filter with up to ˜40 taps (time delays) with adaptive complex coefficients. At the outputs of the MIMO equalizer 270, two complex signals are provided with one sample per symbol. The MIMO equalizer 270 is typically realized in the time domain, although an equivalent frequency-domain implementation can also be used.
In the example shown in FIG. 1, a carrier recovery block 280 computes and applies a phase correction to the signals provided by the MIMO equalizer 270. The phase corrected H and V signals 290, 300 are subsequently de-mapped in a demapper 310 to hard-decided bits in case of hard-decision forward error correction (FEC), or soft bit metrics in case of soft-decision FEC. The output of the demapper 310 can then be provided to a channel decoder 320 for further processing.
FIG. 1 shows a conventional solution for the blind adaptation (without dedicated training symbols) of the MIMO equalizer 270. In this scheme, mismatch errors are estimated in mismatch error estimation blocks 330, 340, 350, 360 based on signals provided by the MIMO equalizer 270, either before or after the carrier recovery 280 has processed the signals. The estimated mismatch errors are then used to adapt the coefficients of the MIMO equalizer 270. For this purpose, selection blocks 370, 380 can be provided to select or merge signals for adapting the coefficients of the MIMO equalizer 270 based on the mismatch errors provided by the mismatch error estimation blocks 330, 340, 350, 360. In the example shown in FIG. 1, the mismatch errors received by the selection blocks 370, 380 can be preprocessed in phase shifting complex conjugating blocks 390, 400.
Typical error criteria derived before phase correction (within the mismatch error estimation blocks 330, 340 shown in FIG. 1) are the stop-and-go algorithm, the constant modulus algorithm (CMA) or modifications thereof. After phase correction, the mismatch is computed (within the mismatch error estimation blocks 350, 360 shown in FIG. 1) as the difference between the received samples and the next valid respective constellation symbols, which is known as decision-directed least-mean-square (DD-LMS) algorithm; in this case the error is counter-rotated (within the blocks 390, 400) by the opposite of the carrier phase correction before being passed to the equalizer.
In some implementations, the receiver can initially rely upon an error computed before the carrier recovery, before it switches to a more accurate criterion derived after the phase correction as soon as the carrier recovery converges.
As mentioned above, a timing misalignment (skew) among the electrical baseband tributaries (HI, HQ, VI, VQ) 110, 120, 130, 140 can arise as a consequence of imbalances in the analog paths, such as for example in the analog-to-digital converters (ADCs) 150, 16, 170, 180. Such imperfections in the analog front-end and in the sampling devices 150, 16, 170, 180 impair the quality of the complex baseband signals. In particular, imbalances in the length of the receiver paths result in timing misalignments (skew) between HI and HQ or VI and VQ, which can severely degrade the performance of the receiver when using high-order modulation formats. Skew between homologous H and V components is less critical because it is akin in its effect to polarization mode dispersion (PMD) and can thus be seamlessly compensated by the MIMO equalizer 270.
FIG. 2 shows a penalty chart 500, wherein the penalty caused by the above timing misalignment (skew) is illustrated in terms of optical signal-to-noise ratio (OSNR) 510 for several m-ary quadrature amplitude modulation (mQAM) formats 520 (at a bit-error rate (BER) of 10−3) as a function of a normalized IQ-skew 530. The penalty indicates the increase of OSNR required to keep the BER at a defined level (10−3 in the example) due to the signal distortions as compared with undistorted signals. For example, in order to stay below a maximum penalty of 0.5 dB, the skew must be maintained below 11%, 5% and 3% of the signaling period for the illustrated 4QAM, 16QAM and 64QAM modulation formats, respectively. This represents a challenging requirement at typical signaling rates of 30-35 GHz for any constellations larger than 4QAM. Additionally, the emerging trend towards higher symbol rates is going to exacerbate the problem.
A precise design of the analog circuitry can suffice to maintain the IQ skew below certain thresholds, and can, for example, provide a feasible solution for PDM-4QAM systems running at an information bit rate of ˜100 Gb/s. However, such precision dependent analog circuitry design becomes increasingly prohibitive as the constellation size and the signaling rate grow. Moreover, it is difficult, if not impossible, to predict skew effects arising in such ADCs, which further complicates the analog circuitry design, and can even prevent the appropriate dimensioning of strip lines on the printed circuit board.
A different state-of-the-art approach aims at mitigating the problem using a calibration procedure. Digital samples are captured directly after the ADCs 15, 160, 170, 180 shown in FIG. 1 and are used to measure the skew. Then, the programmable delays 190, 200, 210, 220 are adjusted accordingly in order to compensate for the timing misalignment. In this approach, the configurable delays 190, 200, 210, 220 must be able to shift the digital signal by fractions of the sampling period, for example by interpolating between the samples. A significant disadvantage of this approach is that the respective calibration routine can be time-consuming and dedicated components (capture facility after the ADCs and configurable fractional delays) are required, which increases the complexity of the circuit and digital processor, and also increases the related power consumption. Further, this approach provides a fixed, non-adaptive, compensation, which can be inadequate for many demanding modulation formats. For example, if the skew of the analog circuitry is time-varying, e.g. because of temperature effects, and/or the skew of the ADCs can change at each power cycle, an adaptive compensation is preferred.
The paper “Compensation for In-Phase/Quadrature Imbalance in Coherent-Receiver Front End for Optical Quadrature Amplitude Modulation” by Md. S. Faruk and K. Kikuchi, IEEE Photonics Journal, volume 5, Number 2, April 2013, shows that the MIMO equalizer in the digital signal processing device 600 can be modified as shown in FIG. 3 to adjust any imbalance, including skew, between the I and Q channels. For this purpose, the paper proposes replacing each of four complex-valued FIR filters included within the complex-valued 2×2 MIMO equalizer 270 shown in FIG. 1 with a 2×2 real-valued MIMO equalizer. As a result, the standard complex 2×2 MIMO equalizer 270 is replaced by a real 4×4 MIMO equalizer 610 as shown in FIG. 3, which has separate ports for HI, HQ, VI and VQ signal components provided by Re/Im splitting blocks 620, 630. Differently from a complex equalizer, a real equalizer processes the real and imaginary parts of H and V as distinct signals and can delay them by different time offsets, thereby correcting IQ skew. As shown in FIG. 3, the so filtered real and imaginary parts of each polarization plane are symbolized conceptually for illustration purposes by having multiplier blocks 640 multiply the respective Q components by the imaginary unit j and the subsequent addition of the respective real and imaginary parts. The paper by Faruk and Kikuchi states that any standard adaptation algorithm can be adopted to update the coefficients of the real MIMO equalizer, and the DD-LMS algorithm is further demonstrated in the paper. Also in this respect, since a complex multiplication requires (in a typical realization) four real multiplications and two real additions, the computational burden of a real 4×4 filter is equivalent in terms of the underlying real arithmetic to that of a complex 2×2 filter.
The paper “Blind Equalization of Receiver In-Phase/Quadrature Skew in the Presence of Nyquist Filtering” by M. Paskov, D. Lavery and S. J. Savory, IEEE Photonics Technology Letters, volume 25, number 24 on Dec. 15, 2013, follows a similar approach as proposed by Faruk and Kikuchi, see discussion above and FIG. 3, but suggests computing the error criterion used for MIMO equalizer 610 adaptation before the carrier recovery, adopting the constant modulus algorithm (CMA) for 4QAM and a radially directed equalizer algorithm for higher order QAM.
The limitations of the above approaches proposed by Faruk and Kikuchi and by Paskov, Lavery and Savory are discussed in the following two papers authored by R. Rios-Müller, J. Renaudier and G. Charlet: “Blind Receiver Skew Compensation for Long-Haul Non-Dispersion Managed Systems”, European Conference on Optical Communications in Cannes, France, September 2014 and “Blind Receiver Skew Compensation and Estimation for Long-Haul Non-Dispersion Managed Systems Using Adaptive Equalizer”, Journal of Lightwave Technology, volume 33, number 7, April 2015. As explained in these papers, the receiver of FIG. 3 can effectively correct IQ skew arising in the receiver front-end only in the back-to-back configuration. In other words, as soon as the signal is transmitted over an optical link, it experiences GVD that must be compensated in the bulk CD equalizer. In this case, the complex coefficients of the bulk CD equalizers 250, 260 shown in FIG. 3 mix the I and Q components on each polarization plane. It follows that the subsequent real 4×4 MIMO equalizer 610 is prevented from accessing and delaying independently the I and Q components on each polarization plane.
From a mathematical perspective, unifying the bulk CD equalizers 250, 260 and the MIMO equalizer 610 in a single bulk CD MIMO equalization stage seems to provide a feasible solution. In FIG. 3, this corresponds to the removal of the blocks enclosed in the dashed rectangle 650. However, merging both equalization stages into one stage requires the implementation of an adaptive MIMO equalizer including 500-4000 (instead of 1-40) taps, which is impractical. On the one side, the adaptation of such a large number of tap coefficients runs into huge convergence difficulties; and on the other side, the use of a 4×4 bulk CD MIMO equalizer results in double complexity with respect to the state-of-the-art solution having two complex 1×1 bulk CD equalizers.
In view of this, Rios-Müller, Renaudier and Charlet propose a different digital signal processing device 700 as illustrated in FIG. 4. The tributaries (HI, HQ, VI, VQ) 110, 120, 130, 140 are separately processed by four bulk CD equalizers 710, 720, 730, 740 with complex coefficients. In FIG. 4 a zero imaginary part is added 750, 760 to each I tributary and the Q tributaries are multiplied 770, 780 by the imaginary unit to indicate for illustration purposes that they are interpreted and processed as a complex signal. Each output of a bulk CD equalizer 710, 720, 730, 740 is complex but contains contributions from only one tributary. Differently from the digital signal processing device 600 shown in FIG. 3, the complex MIMO equalizer 790 shown in FIG. 4 can delay the tributaries independently and correct a relative timing misalignment also in the presence of GVD. The implementation of the four bulk CD equalizers 710, 720, 730, 740 can be simplified by exploiting the fact that the imaginary part of their input is zero. In fact, it is easy to prove that the four bulk CD equalizers 710, 720, 730, 740 of FIG. 4 require approximately as many computations as the two bulk CD equalizers 250, 260, 620, 630 shown in FIG. 1 or FIG. 3.
However, a significant disadvantage of the arrangement shown in FIG. 4 is that the complex 4×2 MIMO equalizer 790 requires twice as many computations as the standard complex 2×2 MIMO equalizer 270 of FIG. 1 or the real 4×4 MIMO equalizer 610 of FIG. 3.